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You cannot prove "a right angle triangle". You may or may not be able to prove statements about right angled triangles but that will depend on the particular statement.
Its important to prove a hypotheses is wrong as it is to prove it right because when you set out to do a lab, you must make your prediction before you start. When you are finished with the lab, you write your report, and that is the time to either prove or disprove your theory. Science isn't all about getting the right hypothesis or answer; it's more about thinking and understanding.
it doesnt
Yes
From Wikipedia: "...a rectangle is any quadrilateral with four right angles". So there isn't much to prove, that's how the rectangle is defined.